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Algebraic Number Theory
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TLDR
In this paper, Algebraic integral integers, Riemann-Roch theory, Abstract Class Field Theory, Local Class Field theory, Global Class Field and Zeta Functions are discussed.Abstract:
I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta Functions and L-series.read more
Citations
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Journal ArticleDOI
Fading channels: information-theoretic and communications aspects
TL;DR: This paper describes the statistical models of fading channels which are frequently used in the analysis and design of communication systems, and focuses on the information theory of fading channel, by emphasizing capacity as the most important performance measure.
BookDOI
Galois theory of linear differential equations
TL;DR: In this paper, a large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, inverse problem and linear differential equations in positive characteristic.
Journal ArticleDOI
Perfect Space–Time Block Codes
TL;DR: The notion of perfect space-time block codes (STBCs) are introduced and algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas are presented.
Book ChapterDOI
Making NTRU as secure as worst-case problems over ideal lattices
Damien Stehlé,Ron Steinfeld +1 more
TL;DR: This work shows how to modify NTRUEncrypt to make it provably secure in the standard model, under the assumed quantum hardness of standard worst-case lattice problems, restricted to a family of lattices related to some cyclotomic fields.
Journal ArticleDOI
On fast multiplication of polynomials over arbitrary algebras
David G. Cantor,Erich Kaltofen +1 more
TL;DR: This paper generalizes the well-known Sch6nhage-Strassen algorithm for multiplying large integers to an algorithm for dividing polynomials with coefficients from an arbitrary, not necessarily commutative, not always associative, algebra d, and obtains a method not requiring division that is valid for any algebra.
References
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Book
The Arithmetic of Elliptic Curves
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Book
An Introduction to Homological Algebra
TL;DR: An Introduction to Homological Algebra as discussed by the authors discusses the origins of algebraic topology and presents the study of homological algebra as a two-stage affair: first, one must learn the language of Ext and Tor and what it describes.
Book
A Course in Arithmetic
TL;DR: In this article, the theorem on arithmetic progressions modular forms is proved for finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratics forms with discriminant +-1.
Book
Advanced Topics in the Arithmetic of Elliptic Curves
TL;DR: In this article, the authors continue the study of elliptic curves by presenting six important, but somewhat more specialized topics: Elliptic and modular functions for the full modular group.